# Marginal value theorem

The marginal value theorem (MVT) is an optimality model that usually describes the behavior of an optimally foraging individual in a system where resources (often food) are located in discrete patches separated by areas with no resources. Due to the resource-free space, animals must spend time traveling between patches. The MVT can also be applied to other situations in which organisms face diminishing returns.

The MVT was first proposed by Eric Charnov in 1976. In his original formulation: "The predator should leave the patch it is presently in when the marginal capture rate in the patch drops to the average capture rate for the habitat."[1]

## Definition

All animals must forage for food in order to meet their energetic needs, but doing so is energetically costly. It is assumed that evolution by natural selection results in animals utilizing the most economic and efficient strategy to balance energy gain and consumption. The Marginal Value Theorem is an optimality model that describes the strategy that maximizes gain per unit time in systems where resources, and thus rate of returns, decrease with time.[2] The model weighs benefits and costs and is used to predict giving up time and giving up density. Giving up time (GUT) is the interval of time between when the animal last feeds and when it leaves the patch. Giving up density (GUD) is the food density within a patch when the animal will choose to move on to other food patches.

When an animal is foraging in a system where food sources are patchily distributed, the MVT can be used to predict how much time an individual will spend searching for a particular patch before moving on to a new one. In general, individuals will stay longer if (1) patches are farther apart or (2) current patches are poor in resources. Both situations increase the ratio of travel cost to foraging benefit.

The optimal time spent in a patch is given by the tangent to the resource intake curve that departs from the expected transit time value. Any other line crossing the resource intake curve has a shallower slope and thus a sub-optimal resource intake rate.

## Modeling

As animals forage in patchy systems, they balance resource intake, traveling time, and foraging time. Resource intake within a patch diminishes with time, as shown by the solid curve in the graph to the right. The curve follows this pattern because resource intake is initially very fast, but slows as the resource is depleted. Traveling time is shown by the distance from the leftmost vertical dotted line to the y-axis. Optimal foraging time is modeled by connecting this point on the x-axis tangentially to the resource intake curve. Doing so maximizes the ratio between resource intake and time spent foraging and traveling.

At the extremes of the loading curve, animals spend too much time traveling for a small payoff, or they search too long in a given patch for an ineffective load. The MVT identifies the best possible intermediate between these extremes.

### Assumptions

1. The individual is assumed to control when it leaves the patch in order to maximize the ratio between resource intake and time.
2. The consumer depletes the amount of resources in the patch where he/she is foraging; therefore, the rate of intake of food in that patch decreases as a function of time.
3. If there is variation in the quality of patches, the MVT assumes that different patches are distributed randomly throughout the landscape.

## Examples

### Humans

A common illustration of the MVT is apple picking in humans. When one first arrives at a new apple tree, the number of apples picked per minute is high, but it rapidly decreases as the lowest-hanging fruits are depleted. Strategies in which too few apples are picked from each tree or where each tree is exhausted are suboptimal because they result, respectively, in time lost travelling among trees or picking the hard to find last few apples from a tree. The optimal time spent picking apples in each tree is thus a compromise between these two strategies, which can be quantitatively found using the MVT.

### Optimal foraging in great tits

Great tits are a species of bird found throughout Europe, northern Africa, and Asia. They are known to forage in “patchy” environments, and research has shown that their behavior can be modeled by optimal foraging models, including the MVT. In a 1977 study by R.A. Cowie,[3] birds were deprived of food and then allowed to forage through patches in two different environments (the environments differed only in distance between patches). As predicted, in both cases birds spent more time in one area when the patches were farther away or yielded more benefits, regardless of the environment. In a similar experiment by Naef-Daenzer (1999),[4] great tits were shown to have a foraging efficiency 30% better than random foraging would yield. This is because great tits were specifically spending more time in resource-rich areas, as predicted by the MVT. This data supports the use of the MVT in predicting the foraging behavior of great tits.

### Feeding in hairy armadillos and guinea pigs

Experimental evidence has shown that screaming hairy armadillos and guinea pigs qualitatively follow MVT when foraging.[5] The researchers ran several parallel experiments: one for each animal under consistent patch quality, and one for guinea pigs with varying patch quality. While the qualitative foraging trend was shown to follow MVT in each case, the quantitative analysis indicated that each patch was exploited further than expected.

### Plant root growth

The MVT can be used to model foraging in plants as well as animals. Plants have been shown to preferentially place their roots, which are their foraging organs, in areas of higher resource concentration. Recall that the MVT predicts that animals will forage for longer in patches with higher resource quality. Plants increase root biomass in layers/areas of soil that are rich in nutrients and resources, and decrease root growth into areas of poor-quality soil. Thus, plants grow roots into patches of soil according to their wealth of resources in a manner consistent with the MVT.[6] Additionally, plant roots grow more quickly through low-quality patches of soil than through high-quality patches of soil, just as foraging animals are predicted to spend less time in low-quality areas than high-quality areas.

### Copulation time in dung flies

The MVT can be applied to situations other than foraging in which animals experience diminished returns. Consider, for example, the mating copulation duration of the yellow dung fly. In the dung fly mating system, males gather on fresh cow droppings and wait for females to arrive in smaller groups to lay their eggs. Males must compete with each other for the chance to mate with arriving females—sometimes one male will kick another male off of a female and take over mating with the female mid-copulation. In this instance, the second male fertilizes about 80% of the eggs.[7] Thus, after a male has mated with a female he guards her so that no other males will have the opportunity to mate with her and displace his sperm before she lays her eggs. After the female lays her eggs, the male must take the time to search for another female before he is able to copulate again.

The question, then, is how long the dung fly should spend copulating with each female. On one hand, the longer a male dung fly copulates the more eggs he can fertilize. However, the benefits of extra copulation time diminish quickly, as the male loses the chance to find another female during long copulations. The MVT predicts that the optimal copulation time is just long enough to fertilize about 80% of the eggs; after this time, the rewards are much smaller and are not worth missing out on another mate.[7] This predicted value for copulation time, 40 minutes, is very close to the average observed value, 36 minutes.

In dung flies, the observed values of copulation time and time searching for another mate vary with body weight. Heavier males have shorter search times and shorter copulation times. These shorter search times are likely due to increased cost of travel with increased body weight; shorter copulation times probably reflect that it is easier for heavier males to successfully take over females mid-copulation. Additionally, researchers have taken into account “patch quality,” i.e. the quality of females arriving on the various cowpats. Research also shows that males copulate for longer with the larger females who hold more eggs and have larger reproductive tract dimensions. Thus, males change their copulation time to maximize their fitness, but they are doing so in response to selection imposed by female morphology. Even with these variations, male dung flies do exhibit close-to-optimal copulation time relative to their body size, as predicted by the MVT.[8]

## Criticism

Many studies, such as the examples presented above, have shown good qualitative support for predictions generated by the Marginal Value Theorem. However, in some more quantitative studies, the predictions of the MVT haven’t been as successful, with the observed values substantially deviating from predictions. One proposed explanation for these deviations is that it is difficult to objectively measure payoff rates. For example, an animal in an unpredictable environment may need to spend extra time sampling, making it hard for researchers to determine foraging time.[9]

Beyond this imprecision, some researchers propose that there is something fundamental missing from the model. Namely, animals are probably doing more than just foraging, whether it be dealing with predation risks or searching for mating opportunities.[9] Natural selection is not the only force influencing the evolution of species. Sexual selection, for example, may alter foraging behaviors, making them less consistent with the MVT. These researchers point out that the marginal value theorem is a starting point, but complexity and nuances must be incorporated into models and tests for foraging and patch-use.

One other type of model that has been used in place of MVT in predicting foraging behavior is the state-dependent behavior model. Although state-dependent models have been viewed as a generalization of the MVT,[10] they are unlikely to generate broadly applicable predictions like those from the MVT because they test predictions under a specific set of conditions. While the predictions of these models must be tested under precise conditions, they might offer valuable insights not available from broader models such as MVT.[9]

## References

1. ^ Charnov, E. L. 1976. Optimal foraging: the marginal value theorem. Theoretical Population Biology 9:129–136
2. ^ Parker, G.A. “Marginal Value Theorem with Exploitation Time Costs: Diet, Sperm Reserves, and Optimal Copula Duration in Dung Flies” (1992) The American Naturalist 139(6):1237–1256
3. ^ Cowie, R. J. (1977) “Optimal foraging in great tits (Parus Major)” Nature 268:137–139
4. ^ Naef-Daenzer, Beat (1999) “Patch time allocation and patch sampling by foraging great and blue tits” Animal Behavior 59:989–999
5. ^ Cassini, Marcelo H., Alejandro Kacelnik, and Enrique T. Segura (1990) “The tale of the screaming hairy armadillo, the guinea pig, and the marginal value theorem” Animal Behavior 39(6):1030–1050
6. ^ McNickle, Gordon G. and James F. Calhill Jr. “Plant root growth and the marginal value theorem” (2009) Proceedings of the National Academ of Sciences of the United States of America 106(12):4747–4751
7. ^ a b Parker, G. A. and R. A. Stuart (1976) “Animal Behavior as a Strategy Optimizer: Evolution of Resource Assessment Strategies and Optimal Emigration Thresholds” The American Naturalist 110(976):1055–1076
8. ^ Parker, Geoffrey A., Leigh W. Simmons, Paula Stockley, Doreen M. McChristie, and Eric L. Charnov. (1999) “Optimal copula duration in yellow dung flies: effects of female size and egg content.” Animal Behavior 57:795–805
9. ^ a b c Nonacs, Peter. “State dependent behavior and the marginal value theorem.” (2001) Behavioral Ecology 12(1):71–83
10. ^ Wajnberg Eric, Pierre Bernhard, Frederic Hamelin and Guy Boivin (2006). "Optimal patch time allocation for time-limited foragers." Behavioral Ecology and Sociobiology, 60, 1–10
Bacterivore

Bacterivores are free-living, generally heterotrophic organisms, exclusively microscopic, which obtain energy and nutrients primarily or entirely from the consumption of bacteria. Many species of amoeba are bacterivores, as well as other types of protozoans. Commonly, all species of bacteria will be prey, but spores of some species, such as Clostridium perfringens, will never be prey, because of their cellular attributes.

Copiotroph

A copiotroph is an organism found in environments rich in nutrients, particularly carbon. They are the opposite to oligotrophs, which survive in much lower carbon concentrations.

Copiotrophic organisms tend to grow in high organic substrate conditions. For example, copiotrophic organisms grow in Sewage lagoons. They grow in organic substrate conditions up to 100x higher than oligotrophs.

Decomposer

Decomposers are organisms that break down dead or decaying organisms, and in doing so, they carry out the natural process of decomposition. Like herbivores and predators, decomposers are heterotrophic, meaning that they use organic substrates to get their energy, carbon and nutrients for growth and development. While the terms decomposer and detritivore are often interchangeably used, detritivores must ingest and digest dead matter via internal processes while decomposers can directly absorb nutrients through chemical and biological processes hence breaking down matter without ingesting it. Thus, invertebrates such as earthworms, woodlice, and sea cucumbers are technically detritivores, not decomposers, since they must ingest nutrients and are unable to absorb them externally.

Dominance (ecology)

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass.

Most ecological communities are defined by their dominant species.

In many examples of wet woodland in western Europe, the dominant tree is alder (Alnus glutinosa).

In temperate bogs, the dominant vegetation is usually species of Sphagnum moss.

Tidal swamps in the tropics are usually dominated by species of mangrove (Rhizophoraceae)

Some sea floor communities are dominated by brittle stars.

Exposed rocky shorelines are dominated by sessile organisms such as barnacles and limpets.

Energy Systems Language

The Energy Systems Language, also referred to as Energese, Energy Circuit Language, or Generic Systems Symbols, was developed by the ecologist Howard T. Odum and colleagues in the 1950s during studies of the tropical forests funded by the United States Atomic Energy Commission. They are used to compose energy flow diagrams in the field of systems ecology.

Eric Charnov

Eric L. Charnov (born October 29, 1947) is an American evolutionary ecologist. He is best known for his work on foraging, especially the marginal value theorem, and life history theory, especially sex allocation and scaling/allometric rules. He is a MacArthur Fellow and a Fellow of the American Academy of Arts and Sciences. Three of his papers are Science Citation Classics.

Charnov gained his B.S. in 1969 from the University of Michigan and his PhD in evolutionary ecology from the University of Washington in 1973. He is a Distinguished Professor (Emeritus) of Biology at the University of New Mexico and the University of Utah.

His research interests are: metabolic ecology (temperature and body size in the determination of biological times and rates), evolutionary ecology (population genetics), evolutionary game theory, and optimization models to understand the evolution of life histories, sex allocation, sexual selection, and foraging decisions.

Feeding frenzy

In ecology, a feeding frenzy occurs when predators are overwhelmed by the amount of prey available. For example, a large school of fish can cause nearby sharks, such as the lemon shark, to enter into a feeding frenzy. This can cause the sharks to go wild, biting anything that moves, including each other or anything else within biting range. Another functional explanation for feeding frenzy is competition amongst predators. This term is most often used when referring to sharks or piranhas. It has also been used as a term within journalism.

Foraging

Foraging is searching for wild food resources. It affects an animal's fitness because it plays an important role in an animal's ability to survive and reproduce. Foraging theory is a branch of behavioral ecology that studies the foraging behavior of animals in response to the environment where the animal lives.

Behavioral ecologists use economic models to understand foraging; many of these models are a type of optimal model. Thus foraging theory is discussed in terms of optimizing a payoff from a foraging decision. The payoff for many of these models is the amount of energy an animal receives per unit time, more specifically, the highest ratio of energetic gain to cost while foraging. Foraging theory predicts that the decisions that maximize energy per unit time and thus deliver the highest payoff will be selected for and persist. Key words used to describe foraging behavior include resources, the elements necessary for survival and reproduction which have a limited supply, predator, any organism that consumes others, and prey, an organism that is eaten in part or whole by another.Behavioral ecologists first tackled this topic in the 1960s and 1970s. Their goal was to quantify and formalize a set of models to test their null hypothesis that animals forage randomly. Important contributions to foraging theory have been made by:

Eric Charnov, who developed the marginal value theorem to predict the behavior of foragers using patches;

Sir Kevin Durant, with work on the optimal diet model in relation to tits and chickadees;

John Gross-Custard, who first tested the optimal diet model against behavior in the field, using redshank, and then proceeded to an extensive study of foraging in the common pied oystercatcher

Herbivore

A herbivore is an animal anatomically and physiologically adapted to eating plant material, for example foliage or marine algae, for the main component of its diet. As a result of their plant diet, herbivorous animals typically have mouthparts adapted to rasping or grinding. Horses and other herbivores have wide flat teeth that are adapted to grinding grass, tree bark, and other tough plant material.

A large percentage of herbivores have mutualistic gut flora that help them digest plant matter, which is more difficult to digest than animal prey. This flora is made up of cellulose-digesting protozoans or bacteria.

Lithoautotroph

A lithoautotroph or chemolithoautotroph is a microbe which derives energy from reduced compounds of mineral origin. Lithoautotrophs are a type of lithotrophs with autotrophic metabolic pathways. Lithoautotrophs are exclusively microbes; macrofauna do not possess the capability to use mineral sources of energy. Most lithoautotrophs belong to the domain Bacteria, while some belong to the domain Archaea. For lithoautotrophic bacteria, only inorganic molecules can be used as energy sources. The term "Lithotroph" is from Greek lithos (λίθος) meaning "rock" and trōphos (τροφοσ) meaning "consumer"; literally, it may be read "eaters of rock". Many lithoautotrophs are extremophiles, but this is not universally so.

Lithoautotrophs are extremely specific in using their energy source. Thus, despite the diversity in using inorganic molecules in order to obtain energy that lithoautotrophs exhibit as a group, one particular lithoautotroph would use only one type of inorganic molecule to get its energy.

MVT

MVT may refer to:

Maldives time, UTC+05:00

Mapnik Vector Tile, vector tile format

The Marchetti MVT, an Italian fighter aircraft of 1919

Marginal value theorem, a behavioral ecology theorem

Marrakesh VIP Treaty

Mean value theorem, a mathematical theorem

Minimum Viable Technology, agile principles applied to engineering/technology teams

Mississippi Valley-Type carbonate hosted lead-zinc ore deposits

Multiprogramming with a Variable number of Tasks, an option of mainframe computer operating system

Multivariate testing (disambiguation)Mvt or mvt or MVT may refer to:

Movement (music), a large division of a larger composition or musical notes

Mesotrophic soil

Mesotrophic soils are soils with a moderate inherent fertility. An indicator of soil fertility is its base status, which is expressed as a ratio relating the major nutrient cations (calcium, magnesium, potassium and sodium) found there to the soil's clay percentage. This is commonly expressed in hundredths of a mole of cations per kilogram of clay, i.e. cmol (+) kg−1 clay.

Mycotroph

A mycotroph is a plant that gets all or part of its carbon, water, or nutrient supply through symbiotic association with fungi. The term can refer to plants that engage in either of two distinct symbioses with fungi:

Many mycotrophs have a mutualistic association with fungi in any of several forms of mycorrhiza. The majority of plant species are mycotrophic in this sense. Examples include Burmanniaceae.

Some mycotrophs are parasitic upon fungi in an association known as myco-heterotrophy.

Optimal foraging theory

Optimal foraging theory (OFT) is a behavioral ecology model that helps predict how an animal behaves when searching for food. Although obtaining food provides the animal with energy, searching for and capturing the food require both energy and time. To maximize fitness, an animal adopts a foraging strategy that provides the most benefit (energy) for the lowest cost, maximizing the net energy gained. OFT helps predict the best strategy that an animal can use to achieve this goal.

OFT is an ecological application of the optimality model. This theory assumes that the most economically advantageous foraging pattern will be selected for in a species through natural selection. When using OFT to model foraging behavior, organisms are said to be maximizing a variable known as the currency, such as the most food per unit time. In addition, the constraints of the environment are other variables that must be considered. Constraints are defined as factors that can limit the forager's ability to maximize the currency. The optimal decision rule, or the organism's best foraging strategy, is defined as the decision that maximizes the currency under the constraints of the environment. Identifying the optimal decision rule is the primary goal of the OFT.

Organotroph

An organotroph is an organism that obtains hydrogen or electrons from organic substrates. This term is used in microbiology to classify and describe organisms based on how they obtain electrons for their respiration processes. Some organotrophs such as animals and many bacteria, are also heterotrophs. Organotrophs can be either anaerobic or aerobic.

Planktivore

A planktivore is an aquatic organism that feeds on planktonic food, including zooplankton and phytoplankton.

Recruitment (biology)

In biology, especially marine biology, recruitment occurs when a juvenile organism joins a population, whether by birth or immigration, usually at a stage whereby the organisms are settled and able to be detected by an observer.There are two types of recruitment: closed and open.In the study of fisheries, recruitment is "the number of fish surviving to enter the fishery or to some life history stage such as settlement or maturity".

Relative abundance distribution

In the field of ecology, the relative abundance distribution (RAD) or species abundance distribution describes the relationship between the number of species observed in a field study as a function of their observed abundance. The graphs obtained in this manner are typically fitted to a Zipf–Mandelbrot law, the exponent of which serves as an index of biodiversity in the ecosystem under study.

Species homogeneity

In ecology, species homogeneity is a lack of biodiversity. Species richness is the fundamental unit in which to assess the homogeneity of an environment. Therefore, any reduction in species richness, especially endemic species, could be argued as advocating the production of a homogenous environment.

General
Producers
Consumers
Decomposers
Microorganisms
Food webs
Example webs
Processes
Defense,
counter
Ecology: Modelling ecosystems: Other components
Population
ecology
Species
Species
interaction
Spatial
ecology
Niche
Other
networks
Other

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.